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Computer Optics

Calculation of quantum characteristics based on the classical solution of the diffraction problem in a resonator with a dielectric plate

IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, С. И. Харитонов, Nikolay Lvovich Kazanskiy, IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, S.G. Volotovsky, IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Svetlana Nikolaevna Khonina, IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS

Published Oct 1, 2022• 2 citations
Publisher

Abstract

The work is devoted to the development of the quantum theory of diffractive optical elements. Aspects of quantum optics are considered by the example of light diffraction from a dielectric plate in a resonator. The paper shows the connection between the classical and quantum solution of the problem of diffraction by a dielectric plate. Expressions are obtained for the eigenmodes of such a resonator, as well as for the operators of the vector magnetic potential and the electric field strength. The method proposed in this paper can be easily extended to dielectric plates with a diffractive microrelief, that is, to diffractive optical elements.

DOI
10.18287/2412-6179-co-1174

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We discuss the quantum fluctuations of the fields associated with a broad class of optical scattering and transmission problems by developing the quantum electrodynamics of an idealized linear, but nonuniform, dielectric medium. We present and compare two quantization schemes for this purpose. The first is based on the expansion of the field in terms of a set of single-frequency solutions of the Maxwell equations. The second involves expanding the field in the set of plane-wave solutions of the Maxwell equations in the vacuum. The relation between the two quantization schemes is discussed in the framework of the scattering theory that connects them. The methods presented are used to show that various field components within a dielectric medium may be either superfluctuant or subfluctuant relative to their fundamental uncertainties in the vacuum. These alterations of the fluctuation properties of the fields are shown to lead to changes in the spontaneous emission rates for both electric and magnetic dipole transitions of excited atoms within or near dielectric media. We also analyze the quantum properties of the transition radiation emitted by a fast charged particle in passing from one dielectric medium to another.
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Starting from a quantum Maxwell equation for the vector potential operator, we study the spontaneous emission properties of a two-level atom interacting with the electromagnetic field in a lossless and inhomogeneous dielectric structure and express the spontaneous emission rate, the external quantum efficiency, and the spontaneous emission factor in terms of the classical Green function of the dielectric structure. Comparing these results with the corresponding classical results, we show that the above quantities can be calculated from the radiation field of a classical dipole. Based on this correspondence, a numerical algorithm is developed to calculate the modification of spontaneous emission in microcavities. The line shape of the emission spectrum of the light source and the decay of the cavity resonant modes are automatically taken into account in this algorithm. The approximate expressions for the spontaneous emission rate and the spontaneous emission factor are discussed.
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